On the generalization of the Kruskal-Szekeres coordinates: a global conformal charting of the Reissner-Nordstrom spacetime

2023/09/18 by Fawzi, Ali, Stojkovic, Dejan
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2309.10123

Abstract

The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the t-line associated with the asymptotic observer into a single point, at the event horizon r=2M. Starting from this point, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner-Nordström manifold, M_RN. We develop a new method for constructing Kruskal-like coordinates and find two algebraically distinct classes charting M_RN. We pedagogically illustrate our method by constructing two compact, conformal, and global coordinate systems labeled \mathcalGK_I and \mathcalGK_II for each class respectively. In both coordinates, the metric differentiability can be promoted to C^∞. The conformal metric factor can be explicitly written in terms of the original t and r coordinates for both charts.

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